Calibration system and method  to align a 3d virtual scene and a 3d real world for a stereoscopic head-mounted display

ABSTRACT

A calibration platform may obtain measurements for aligning a real-world coordinate system and a display coordinate system. For example, the calibration platform may display, via an optical see-through head-mounted display (OST-HMD), a three-dimensional virtual object and receive, from a positional tracking device, information that relates to a current pose of a three-dimensional real-world object to be aligned with the three-dimensional virtual object. The calibration platform may record a three-dimensional position of a plurality of points on the three-dimensional real-world object based on the current pose of the three-dimensional real-world object, based on an indication that the plurality of points on the three-dimensional real-world object respectively corresponds with a plurality of points on the three-dimensional virtual object. Accordingly, based on the obtained measurements, the calibration platform may generate a transformation function to provide a mapping between three-dimensional points in the real-world coordinate system and three-dimensional points in the display coordinate system.

RELATED APPLICATION(S)

This application claims priority under 35 U.S.C. § 119 to U.S. Provisional Patent Application No. 62/625,980, filed on Feb. 3, 2018, the content of which is incorporated by reference herein in its entirety.

GOVERNMENT LICENSE RIGHTS

This invention was made with U.S. Government support under grant W81XWH-15-C-0156, awarded by the Department of Defense. The U.S. Government has certain rights in the invention.

BACKGROUND

An optical head-mounted display, sometimes referred to as an optical see-through head-mounted display (OST-HMD), is a wearable device that can reflect projected images onto one or more screens while also allowing a user wearing the OST-HMD to see through the screen(s). For example, a typical OST-HMD uses an optical mixer made from partly silvered mirrors to reflect artificial (e.g., computer-generated) images and allow real images to cross the lens. Accordingly, OST-HMDs are increasingly being used for augmented reality and/or mixed reality applications. “Augmented reality” generally refers to interactive technologies in which objects in a real-world environment are “augmented” using computer-generated virtual content that may be overlaid on the real-world environment. “Mixed reality,” sometimes referred to as “hybrid reality,” similarly merges real and virtual worlds to produce a visual environment in which real physical objects and virtual digital objects can co-exist. However, in addition to overlaying virtual objects on the real-world environment, mixed reality applications often anchor the virtual objects to the real-world and allow users to interact with the virtual objects.

SUMMARY

According to some implementations, a method may comprise obtaining, by a calibration platform, a set of measurements for aligning a real-world coordinate system associated with a positional tracking device and a display coordinate system corresponding to a three-dimensional display space of an optical see-through head-mounted display device. In some implementations, obtaining the set of measurements may comprise causing, by the calibration platform, the optical see-through head-mounted display device to display a three-dimensional virtual object in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device; receiving, at the calibration platform, information from the positional tracking device that relates to a current pose of a three-dimensional real-world object to be aligned with the three-dimensional virtual object; recording, by the calibration platform, a three-dimensional position of a plurality of points on the three-dimensional real-world object in the real-world coordinate system based on the current pose of the three-dimensional real-world object, based on an indication that the plurality of points on the three-dimensional real-world object respectively corresponds with a plurality of points on the three-dimensional virtual object; and generating the set of measurements based on the three-dimensional position of the plurality of points on the three-dimensional real-world object in the real-world coordinate system. In some implementations, the method may further comprise generating, by the calibration platform, a transformation function that permits the calibration platform to provide a mapping between three-dimensional points in the real-world coordinate system and three-dimensional points in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device based on the set of measurements.

According to some implementations, a calibration device may comprise a memory and one or more processors communicatively coupled to the memory. In some implementations, the one or more processors may receive, from a positional tracking device, information that relates to a pose of a three-dimensional real-world object to be aligned with a three-dimensional virtual object. The one or more processors may perform a first operation to display, via an optical see-through head-mounted display device, the three-dimensional virtual object in a display coordinate system corresponding to a three-dimensional display space of the optical see-through head-mounted display device, and perform a second operation to record three-dimensional positions of multiple points on the three-dimensional real-world object in a real-world coordinate system associated with the positional tracking device based on the pose of the three-dimensional real-world object at a time when a calibration input is received. The first operation and the second operation may be repeated until a recorded quantity of the three-dimensional positions satisfies a threshold value, and the one or more processors may generate a transformation function providing a mapping between three-dimensional points in the real-world coordinate system and three-dimensional points in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device, based on the recorded quantity of the three-dimensional positions.

According to some implementations, a non-transitory computer-readable medium may store instructions comprising one or more instructions that, when executed by one or more processors, cause the one or more processors to generate a transformation function providing a mapping between three-dimensional points in a real-world coordinate system and three-dimensional points in a display coordinate system corresponding to a three-dimensional display space of an optical see-through head-mounted display device, based on a set of measurements gathered using a positional tracking device. The one or more instructions, when executed by the one or more processors, may further cause the one or more processors to apply the transformation function to a first internal projection operator to produce a first corrected projection operator that the optical see-through head-mounted display device uses to display a first two-dimensional perspective image for a left eye, and apply the transformation function to a second internal projection operator to produce a second corrected projection operator that the optical see-through head-mounted display device uses to display a second two-dimensional perspective image for a right eye. In some implementations, the one or more instructions, when executed by the one or more processors, may further cause the one or more processors to display, via the optical see-through head-mounted display device, a three-dimensional image in the display coordinate system by presenting the first two-dimensional perspective image based on the first corrected projection operator and presenting the second two-dimensional perspective image based on the second corrected projection operator, wherein the three-dimensional image in the display coordinate system may be superimposed on an object in the real-world coordinate system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1B, 2A-2B, 3-4, 5A-5B, and 6-7 are diagrams of one or more example implementations described herein.

FIG. 8 is a diagram of an example environment in which systems and/or methods described herein may be implemented.

FIG. 9 is a diagram of example components of one or more devices of FIG. 8.

FIGS. 10-12 are flow charts of example processes for aligning a three-dimensional virtual scene and a three-dimensional real world for a stereoscopic head-mounted display device.

DETAILED DESCRIPTION

The following detailed description of example implementations refers to the accompanying drawings. The same reference numbers in different drawings may identify the same or similar elements.

The use of optical see-through head-mounted displays (OST-HMDs) for augmented reality and/or mixed reality applications has increased significantly in recent years. However, one particular area that has remained challenging for these systems is display calibration. For example, because augmented and mixed reality applications are designed to visualize virtual objects in a real-world environment, displaying the virtual objects according to a correct pose and alignment is important for proper user experience in augmented and/or mixed reality applications (e.g., surgical navigation). Proper calibration is also needed to correctly display virtual content anchored to the real-world in order to create a realistic augmented and/or mixed reality experience for other applications, such as training, gaming, and/or the like. However, existing methods intended to improve HMD calibration suffer from various drawbacks.

For example, in many cases there may be limited to no access to internal projection operators (e.g., matrices) that the HMD uses to generate stereoscopic three-dimensional images. To the extent that the internal projection operators are available, the access tends to be limited to a device-dependent transformation from a display screen to tracking coordinates. This means that a transformation chain from the display screen to the user's eye(s) is incomplete. Furthermore, even when an HMD has capabilities to create stable virtual objects in the real-world (e.g., using image-tracking support, spatial mapping capabilities to provide a detailed representation of real-world surfaces in an environment around the HMD, inertial measurement unit (IMU) sensing capabilities that can provide information relating to an orientation of the HMD based on changes in pitch, roll, and yaw, and/or the like), existing calibration methods fall short in aligning virtual content and the view of the user wearing the HMD.

One reason for this is that with an OST-HMD, there is no direct access to the view of the user (i.e., the view of the user essentially exists only in the user's retina). Furthermore, a calibration result is no longer valid when the user changes and/or the OST-HMD is displaced relative to the user's eyes. Therefore, a user-dependent calibration procedure is generally needed to correctly align virtual content with a real-world counterpart. One existing display calibration method is the Single Point Active Alignment Method (SPAAM), in which a user collects 2D-3D point correspondences that are used to calculate a mapping from a 3D point cloud to 2D screen coordinates using a Direct Linear Transform (DLT). However, calibration procedures based on SPAAM are designed to calibrate one screen of the OST-HMD and one eye of the user at a given time. Thus, to ensure that rendered graphics on a stereoscopic OST-HMD are correctly aligned with the user's two eyes, the calibration procedure would need to be performed twice (once for each eye), which can lead to fatigue and inaccuracy caused by such repetition. Although the Stereo-SPAAM variant of SPAAM can simultaneously calibrate both eyes with a stereoscopic OST-HMD by adding physical constraints of two eyes (e.g., an interpupillary distance (IPD)), Stereo-SPAAM nonetheless finds the projection operator from the virtual camera formed by the eye to the planar screen based on two separate 2D-3D mappings that are calculated with the same underlying model. Accordingly, in either case, SPAAM-based calibration methods do not account for the fact that the user is perceiving a 3D scene rather than two 2D planar screens.

Some implementations described herein relate to calibrating an OST-HMD according to an approach that takes data from a positional tracking device as an input and produces 3D coordinates of a virtual object in the eyes of a user wearing the OST-HMD as an output based on a 3D-to-3D projection that aligns the virtual object with a real-world counterpart object. More particularly, in some implementations, a user wearing the OST-HMD may be given a real object to be aligned with a counterpart virtual object. For example, in some implementations, the real object may be a physical object having fiducial markers to aid in tracking the real object, colored faces to aid in the alignment task, and/or the like. Additionally, or alternatively, the real object may be an asymmetrical object to avoid potential problems relating to ambiguities in features (e.g., different corners that have the same or a substantially similar appearance) and to permit the calibration procedure to be used in monochromatic settings.

In some implementations, during the calibration procedure the virtual object may be displayed in a manner whereby the virtual object is initially misaligned with the real object. Accordingly, the user may be tasked with aligning one or more points (e.g., one or more corners) on the real object with one or more corresponding points on the virtual object (e.g., by moving the real object around in space, by moving the user's head or otherwise shifting positions, and/or the like). A positional tracking device (e.g., a head-anchored tracking device, a world-anchored tracking device, and/or the like) may be configured to track real-world coordinates associated with the real object. Accordingly, when the user provides an input to indicate that the one or more points on the real object and the one or more corresponding points on the virtual object are aligned in the user's view, the real-world coordinates associated with the one or more points on the real object, as tracked by the positional tracking device, may be recorded. This process may be repeated until a threshold quantity of measurements have been obtained, at which point a transformation function that corrects misalignments of the real object with the virtual counterpart in the user's eyes may be calculated (e.g., based on one or more 3D projection operators). In this way, the transformation function can be used to represent virtual objects in the same coordinate system as real-world objects, which may create a more realistic and immersive augmented and/or mixed reality experience. Furthermore, in this way, when a position and/or orientation of one or more real-world objects changes in the user's view, any virtual content that is overlaid on the one or more real-world objects may remain anchored to the one or more real-world objects.

In some implementations, the calibration procedure may task the user with aligning one point on the real object with one point on the virtual object each time that the alignment procedure is performed until the threshold quantity of measurements have been obtained. Additionally, or alternatively, the user may be instructed to simultaneously align multiple points on the real-world object and multiple corresponding points on the virtual object. In this way, fewer repetitions may be needed to obtain the threshold quantity of measurements, which may increase accuracy by avoiding user fatigue that may occur over multiple repetitions while also making the calibration procedure substantially easier and faster (and thus conserving memory, processing, and/or other resources) relative to an approach that collects one point at a time.

FIGS. 1A-1B are diagrams of one or more example implementations 100, 110 described herein. FIGS. 1A-1B show schematic views of misalignment between a tracking space (e.g., a real-world coordinate space tracked by a positional tracking device) and a display space (e.g., a display coordinate space in which an OST-HMD renders a three-dimensional virtual scene that may include one or more virtual objects). As mentioned above, because augmented and/or mixed reality applications are designed to visualize virtual objects in reality, a correct pose and alignment of the virtual objects to be rendered is important for a proper user experience. For example, if the OST-HMD in example implementations 100, 110 is not calibrated with the positional tracking device, the misalignment between the tracking space and the display space will cause an unrealistic and/or undesirable augmented and/or mixed reality experience. Accordingly, in some implementations, a calibration procedure may be used to compute a transformation function that enables the OST-HMD to represent virtual objects in the same coordinate system as real-world objects (e.g., by aligning the display coordinate space in which the OST-HMD renders the virtual objects with the real-world coordinate space tracked by the positional tracking device). For example, given a real-world cube and a virtual cube to be overlaid on the real-world cube, the transformation function may be used to move, warp, and/or otherwise adjust a rendering of the virtual cube such that the virtual cube and the real-world cube are aligned. In another example, given a real-world cup and a virtual lid to be placed on the real-world cup, the transformation function may be used to move, warp, or otherwise adjust the rendering of the virtual lid in the display space to remain aligned with the top of the real-world cup. Moreover, as described in further detail herein, the calibration procedure can be used to compute the transformation function using a head-anchored tracking device (e.g., as shown in FIG. 1A) and/or a world-anchored tracking device (e.g., as shown in FIG. 1B).

As shown in FIG. 1A, example implementation 100 may include an OST-HMD (e.g., a stereoscopic OST-HMD) that can generate a three-dimensional image in the display space by presenting a pair of two-dimensional perspective images of a three-dimensional virtual scene (e.g., a first perspective image for a left eye and a second perspective image for a right eye). For example, in some implementations, the OST-HMD may present the pair of two-dimensional perspective images from two slightly different viewing positions using a left eye projection operator and a right eye projection operator.

As further shown in FIG. 1A, example implementation 100 may include a head-anchored tracking device that can perform “inside-out” positional tracking. For example, in some implementations, the head-anchored tracking device may be a front-facing camera embedded in the OST-HMD, a camera and/or other sensors rigidly mounted on the OST-HMD, and/or the like. In some implementations, the head-mounted tracking device may have a similar line of sight as the user wearing the OST-HMD and may generally track a position of the OST-HMD in a three-dimensional Euclidean tracking space. For example, when the OST-HMD moves, the head-mounted tracking device may readjust the tracked position of the OST-HMD (e.g., based on translational movements, changes in pitch, roll, and yaw, and/or the like).

In some implementations, the head-mounted tracking device may further track three-dimensional positions of real-world objects based on observed features of the surrounding environment using a marker-based tracking algorithm that offers simplicity and robustness, and/or a marker-free (or marker-less) tracking algorithm that offers better user experience. For example, when the marker-based tracking algorithm is used, real-world objects may have one or more fiducial markers (e.g., primitive shapes such as points, squares, circles, and/or the like) that are designed to be easily detected and serve as reference points for the head-mounted tracking device. Additionally, or alternatively, the head-mounted tracking device may perform inside-out positional tracking using infrared (IR) markers and a camera that is sensitive to IR light. When using the marker-free tracking algorithm, the head-mounted tracking device may use distinctive characteristics that originally exist in the real-world environment to determine position and orientation. Relative to a world-anchored tracking device, the head-mounted tracking device may have a reduced size, consume less power, and/or have a smaller computational cost.

As shown in FIG. 1B, example implementation 110 may also include an OST-HMD (e.g., a stereoscopic OST-HMD) that can generate a three-dimensional image by presenting a pair of perspective images of a three-dimensional scene from two slightly different viewing positions using a left eye projection operator and a right eye projection operator.

As further shown in FIG. 1B, example implementation 110 may include a world-anchored tracking device that can perform “outside-in” positional tracking. For example, in some implementations, the world-anchored tracking device may be a reflective marker tracking device, an electromagnetic sensing tracking device, a projective light-based tracking device, and/or the like. In the world-anchored tracking device, a tracking coordinate system may have a fixed pose with respect to a real-world coordinate system. Accordingly, in some implementations, the world-anchored tracking device may use spatial mapping capabilities associated with the OST-HMD (e.g., based on a simultaneous localization and mapping (SLAM) technique) to obtain a pose of the OST-HMD with respect to the world-anchored tracking device. Additionally, or alternatively, one or more markers (e.g., fiducial markers) may be attached to the OST-HMD and used to track the pose of the OST-HMD.

In some implementations, as noted above, the world-anchored tracking device may perform outside-in positional tracking to trace three-dimensional scene coordinates of real-world objects (e.g., the OST-HMD and/or other real-world objects in the surrounding environment). The world-anchored tracking device may include one or more cameras and/or other sensors that are placed in a stationary location and oriented towards the tracked real-world object(s) that are allowed to move freely around an area defined by intersecting visual ranges of the cameras. Like the head-anchored tracking device in implementation 100, the world-anchored tracking device may track real-world objects that have a set of markers (e.g., fiducial markers, infrared (IR) markers, and/or the like) and/or marker-free real-world objects. Relative to the head-anchored tracking device, the world-anchored tracking device can potentially be more accurate because the world-anchored tracking device may not have the same constraints as the head-anchored tracking device with respect to size, power consumption, computational resources, type of technology used, and/or the like. Furthermore, when the OST-HMD has self-localization and/or spatial mapping capabilities that can provide the pose of the OST-HMD, the world-anchored tracking device may be able to track real-world objects in the tracking space even when there is no direct line of sight from the camera of the OST-HMD to the tracked real-world objects.

In some implementations, as mentioned above, in implementations 100, 110, a calibration procedure may be used to compute a transformation function that enables the OST-HMD to represent virtual objects in the same coordinate system as real-world objects (e.g., by aligning the display space with the tracking space). For example, the transformation function may be computed using a set of measurements gathered using the head-anchored tracking device, the world-anchored tracking device, and/or the like. More particularly, the calibration procedure may use the set of measurements to compute a transformation function that provides a mapping between three-dimensional points in a real-world coordinate system (e.g., the tracking space) and corresponding points in a three-dimensional virtual environment (e.g., the display space). Accordingly, the transformation function may be applied to default internal projection operators that the OST-HMD uses to generate a three-dimensional image based on two-dimensional perspective images that are presented for each of the user's eye, resulting in corrected projection operators that effectively adjust the default internal projection operators to correct misalignments in visualizing virtual objects in the display space with respect to real-world objects in the tracking space.

As indicated above, FIGS. 1A-1B are provided merely as one or more examples. Other examples may differ from what is described with regard to FIGS. 1A-1B.

FIGS. 2A-2B are diagrams of one or more example implementations 200 described herein. More particularly, in implementation(s) 200, a calibration platform may perform a calibration procedure to solve a transformation function T(⋅) that provides a mapping between three-dimensional points in a real-world coordinate system tracked by a positional tracking device and corresponding points in a three-dimensional virtual scene visualized by an HMD (e.g., an OST-HMD) worn by a user. For example, given the points q₁, . . . , q_(n) in the real-world coordinate system, the calibration platform may compute the transformation function T(⋅) to map the points q₁, . . . , q_(n) in the real-world coordinate system to corresponding points p₁, . . . , p_(n) in a display coordinate system as follows:

p _(i) =T(q _(i)) i=1, . . . ,n.

In some implementations, the calibration procedure may be performed based on an assumption that both p_(i) and q_(i)∈

³ (e.g., p_(i) and q_(i) are both elements of a three-dimensional coordinate space). Accordingly, the calibration platform may estimate T based on a set of measurements (or observations) in the form of (q_(i), p_(i)) for i=1, . . . , n. More specifically, the measurement of q_(i) may be obtained using the positional tracking device, while p_(i) is pre-defined and visualized on the OST-HMD worn by the user. Accordingly, with the calculated transformation function T(⋅), a point in the real-world coordinate system tracked by the positional tracking device can be mapped to a corresponding point in the display coordinate system. In this way, the transformation function may correct misalignments of real objects with virtual counterparts in the user's eyes such that virtual objects and real-world objects can be represented in a common coordinate system.

As shown in FIG. 2A, and by reference number 210, a calibration object with one or more fiducial markers may be given to a user wearing the OST-HMD. For example, in some implementations, the calibration object may be a cube with different fiducial markers attached on faces of the cube to aid the positional tracking device in tracking the real-world coordinates of the calibration object. Additionally, or alternatively, each face of the calibration object may have a different color to make an alignment task more intuitive. In some implementations, using a cube with fiducial markers and colored faces as the calibration object may provide the user with additional depth cues utilizing unique depth cue characteristics of three-dimensional visualization. As further shown in FIG. 2A, and by reference number 220, the calibration object provided to the user may additionally, or alternatively, be an asymmetrical calibration object. In this way, the asymmetrical calibration object may not have ambiguous corners (as in a cube), which may obviate a need to use different colors on the faces of the calibration object. In this way, the asymmetrical calibration object can be used in a monochromatic setting. Furthermore, the calibration object may have a stem and/or another suitable member to be held by the user, which may reduce the effects of poor alignment, hand tremor, and/or the like.

As shown in FIG. 2A, and by reference number 230, the calibration platform may provide, to the OST-HMD worn by the user, a virtual image to be overlaid on the calibration object for the calibration procedure. For example, the virtual image may be a three-dimensional virtual object that has the same shape as the calibration object and/or additional visual characteristics that aid the user in aligning the calibration object and the virtual object (e.g., colored faces that match the colored faces of the calibration object). Additionally, or alternatively, the virtual object may have a feature (e.g., a corner, an edge, and/or the like) that the user is tasked with aligning with one or more features on the calibration object. As shown in FIG. 2A, and by reference number 240, the OST-HMD may display the virtual object in a field of view of the user wearing the OST-HMD. In some implementations, the virtual object may be displayed in a location that is not correctly aligned with the calibration object. As shown in FIG. 2A, and by reference number 250, the calibration platform may instruct the user (e.g., via an automated voice command or screen prompt) to align one or more features of the virtual object with one or more corresponding features in the real-world (e.g., a corner, an edge, and/or another suitable feature of the calibration object).

In particular, the user may move the calibration object around in space, shift the user's head and/or body position, and/or the like until the user is satisfied that the calibration object and the virtual object are aligned in the user's view. For example, the implementation(s) 200 shown in FIG. 2A illustrate a multi-point alignment example in which the user is instructed to align multiple features (e.g., five corners) of the calibration object and multiple corresponding features of the virtual object. Additionally, or alternatively, the multi-point alignment example may instruct the user to align more than five points on the calibration object and the virtual object (e.g., the user could be instructed to align all seven corners of the cube that are visible). Additionally, or alternatively, the multi-point alignment example may instruct the user to align fewer than five points on the calibration object and the virtual object, as three (3) non-collinear and/or non-coplanar points in space are generally sufficient to fully determine a pose of a three-dimensional object. However, using more than three points (e.g., five in the illustrated example) may make the alignment task easier, provide the user with a better depth cue, and/or reduce a quantity of repetitions to be performed to obtain a threshold quantity of alignment measurements for computing the transformation function.

Additionally, or alternatively, implementation(s) 200 may utilize a single point alignment in which the user is instructed to align only one feature (e.g., one corner) of the calibration object and the virtual object. In this way, the positional tracking device may measure the three-dimensional position of only the one feature, which may reduce the burden associated with each alignment repetition. However, the single point alignment may need more repetitions to obtain the threshold quantity of alignment measurements, which can lead to inaccuracy due to user fatigue.

As shown in FIG. 2A, and by reference number 260, the positional tracking device may provide one or more alignment measurements to the calibration platform based on an input from the user indicating that the appropriate feature(s) on the calibration object and the virtual object appear to be aligned in the user's view. For example, the input from the user may be a button press, a mouse click, a voice command, a hand motion, a gesture, and/or the like. In some implementations, the virtual object may then appear in another location in the field of view of the user and the user may be instructed to perform the alignment task again. This process may be repeated until the threshold number of alignment measurements are obtained (e.g., ˜20 measurements, which may be obtained in just four repetitions in the five-point alignment example). In some implementations, the virtual object may be displayed in a different location for each repetition, to cover as much of an area within the user's reach as possible. In this way, the alignment measurements used to compute the transformation function may be more balanced and less biased toward any given geometrical location.

As shown in FIG. 2A, and by reference number 270, the calibration platform may compute the transformation function based on the threshold quantity of alignment measurements provided by the positional tracking device. More specifically, as mentioned above, the calibration platform may estimate the transformation function (T) based on a set of measurements (or observations) in the form of (q_(i), p_(i)) for i=1, . . . , n, where the measurement of q_(i) is a three-dimensional point obtained from the positional tracking device (e.g., a three-dimensional position of a point on the calibration object to be aligned with a corresponding point on the virtual object), while p_(i) is pre-defined and visualized on the OST-HMD (e.g., a three-dimensional position at which the corresponding point on the virtual object is visualized).

In some implementations, the transformation function computed by the calibration platform may be a linear transformation function. For example, because the aim is to find a transformation between a three-dimensional coordinate system associated with the positional tracking device and a three-dimensional display coordinate system associated with a display space of the OST-HMD, the calibration platform may compute the transformation function as an affine transformation with 12 unknown parameters, as the transformation between coordinate systems is affine. Additionally, or alternatively, the calibration platform may solve for a general case where the transformation is a perspective transformation with 15 unknown parameters (excluding an arbitrary scale parameter). Additionally, or alternatively, because fewer unknown parameters require fewer calibration alignments and thus can considerably reduce the burden on the user, the calibration platform may compute the transformation function as an isometric transformation that has 6 unknown parameters.

For example, a 3D-to-3D rigid transformation may generally be represented as:

{circumflex over (p)} _(i)=[T]_(4×4) ·{circumflex over (q)} _(i)

More specifically, the mathematical representation of the affine, perspective, and isometric transformations may be as follows:

i) Affine Transformation:

${{\hat{p}}_{i} = {\left\lbrack T_{A} \right\rbrack_{4 \times 4} \cdot {\hat{q}}_{i}}},{T_{p} = \begin{bmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\ a_{21} & a_{22} & a_{23} & a_{24} \\ a_{31} & a_{32} & a_{33} & a_{34} \\ 0 & 0 & 0 & 1 \end{bmatrix}}$

where the first three rows of T_(A) are arbitrary.

ii) Perspective Transformation:

${{\hat{p}}_{i} = {\left\lbrack T_{p} \right\rbrack_{4 \times 4} \cdot {\hat{q}}_{i}}},{T_{p} = \begin{bmatrix} p_{11} & p_{12} & p_{13} & p_{14} \\ p_{21} & p_{22} & p_{23} & p_{24} \\ p_{31} & p_{32} & p_{33} & p_{34} \\ p_{41} & p_{42} & p_{43} & p_{44} \end{bmatrix}}$

where both {circumflex over (p)}_(i) and {circumflex over (q)}_(i) are represented in normalized homogeneous coordinates and T_(P) is an arbitrary 4×4 matrix with 15 unknown parameters (excluding an arbitrary scale).

iii) Isometric Transformation:

${{\hat{p}}_{i} = {\left\lbrack T_{I} \right\rbrack_{4 \times 4} \cdot {\hat{q}}_{i}}},{T_{I} = \begin{bmatrix} r_{11} & r_{12} & r_{13} & i_{1} \\ r_{21} & r_{22} & r_{23} & i_{2} \\ r_{31} & r_{32} & r_{33} & i_{3} \\ 0 & 0 & 0 & 1 \end{bmatrix}}$

where T₁ is composed of a 3×3 orthonormal matrix {r_(i,j)} representing rotation, and a 3×1 translational vector {right arrow over (i)}.

In some implementations, to solve the calibration problem, the calibration platform may compute a transformation function T that minimizes a reprojection error of the set of alignment measurements (E_(reproj)), which is represented as follows:

$E_{reproj} = \frac{\sum\limits_{i = 1}^{n}\;\sqrt{\left( {p_{i} - {T\left( q_{i} \right)}} \right)^{2}}}{n}$

In some implementations, the calibration platform may calculate the affine transformation and/or the perspective transformation using a Direct Linear Transformation (DLT) algorithm, with an objective of minimizing a total algebraic error. For the isometric transformation, the problem is equal to registration of two rigid three-dimensional point sets, whereby an absolute orientation method may be used with an objective of minimizing a least-square error of the registration.

In some implementations, as mentioned above, the OST-HMD generates a three-dimensional image by presenting two two-dimensional perspective images, one for each eye, of a three-dimensional scene from two slightly different viewing positions. Each two-dimensional perspective image has a respective projection operator (P). In some implementations, the projection operator P may be represented by a 3×4 matrix and the OST-HMD may have a default configuration and preset internal projection matrices that can be represented as follows:

-   -   Left Eye Default: [P_(LD)]_(3×4),     -   Right Eye Default: [P_(RD)]_(3×4)

In some implementations, the computed transformation, T, may be applied to each of the left eye default projection operator and the right eye default projection operator, which may result in the following effective left eye and right eye projection matrices in implementations where the projection operator P is represented by a 3×4 matrix:

[P _(LE)]_(3×4)=[P _(LD)]_(3×4)·[T]_(4×4)

[P _(RE)]_(3×4)=[P _(RD)]_(3×4)·[T]_(4×4)

Accordingly, the computed transformation, T, may effectively adjust the default internal projection operators used in the OST-HMD to correct misalignments in visualizing virtual objects with respect to a real scene. In other words, the computed elements in the effective projection operators may adjust an original or default calibration associated with the OST-HMD (e.g., with respect to aspect ratio, focal length, extrinsic transformation, and/or the like). In general, a 3×4 projection matrix contains eleven degrees of freedom (e.g., six for camera extrinsics and five for camera intrinsics). For stereo visualization, one common approach is to use the same projection matrix for both eyes, except with a translation (obtained using the interpupillary distance) along one coordinate direction, for a total of twelve degrees of freedom. Accordingly, while the different types of transformations (e.g., isometric, affine, and perspective) may all be 3D-3D transformations (i.e., each transformation takes a 3D point as an input and produces a 3D point as an output), the different types of transformations may vary in the number of degrees of freedom and the manner and/or extent to which the transformations can adjust the default projection matrices. For example, the isometric transformation is more constrained with six (6) parameters to estimate and maintains the dimensions (e.g., distances and angles) of the virtual objects to be displayed and merely changes the pose (e.g., the position and/or orientation) of the virtual objects. The affine transformation is less constrained than the isometric transformation with twelve (12) parameters to estimate and preserves parallel lines while warping (e.g., stretching and/or shearing) the shape of the virtual objects. The perspective transformation is the least constrained with fifteen (15) parameters to estimate and preserves collinearity, cross-ratio, order of points, and/or the like.

In some implementations, the calibration platform may analyze an error that results from each of the affine, perspective, and isometric transformations to determine which one represents a most accurate model. For example, because the alignment task is performed by a human user and thus is prone to error (e.g., because of fatigue due to having to perform multiple repetitions, hand tremor, and/or the like), a Random Sample Consensus (RANSAC) algorithm may be used to find the most accurate transformation and reject outliers based on the reprojection error E_(reproj) of the set of measurements.

In some implementations, as shown in FIG. 2B, the calibration procedure may be performed independently of any internal features of the OST-HMD. For example, as shown in FIG. 2B, different OST-HMDs may use different display technologies, firmware packages, software development kits (SDKs), internal projection operators, and sensor configurations (e.g., built-in sensors, interfaces to external sensors, and/or the like). In particular, the calibration procedure may treat the OST-HMD like a blackbox, using data from a positional tracking system as an input and a visualization of a virtual three-dimensional object in the eyes of an observer (e.g., a user wearing the OST-HMD) as an output. For example, the OST-HMDs may enable the calibration platform to create a three-dimensional visualization of virtual content in a three-dimensional projective virtual space in front of the user's eyes and/or provide access to a final three-dimensional visualization of virtual content. Furthermore, the calibration platform may have access to the data gathered using the positional tracking device.

Accordingly, regardless of a level of access (if any) to internal settings associated with the OST-HMD, the calibration may use the three-dimensional representation of virtual content and the data gathered using the positional tracking device to compute a 3D-to-3D projection that corrects misalignments between real objects and virtual counterparts in the user's eyes (e.g., a 3D-to-3D projection from a three-dimensional Euclidean tracking space tracked by the positional tracking device to a three-dimensional projective virtual space perceived by the user). In this way, regardless of any intermediate processes used in the OST-HMD to create the virtual scene, the calibration procedure may correct the final alignment in the three-dimensional perceived scene, which is what matters for the user and affects the augmented and/or mixed reality experience. Accordingly, from this perspective, the projection computed by the calibration platform is from a three-dimensional real world to a three-dimensional space rather than two planar screens, whereby a mapping model used by the calibration platform becomes a 3D-3D registration procedure (e.g., representing information three-dimensionally in space rather than two-dimensionally within a screen coordinate system).

As indicated above, FIGS. 2A-2B are provided merely as one or more examples. Other examples may differ from what is described with regard to FIGS. 2A-2B.

FIG. 3 is a diagram of an example implementation 300 described herein. FIG. 3 shows a setup for performing the calibration procedure described in further detail above with a head-anchored tracking device configured to perform inside-out positional tracking.

As shown in FIG. 3, implementation 300 may use a front-facing camera embedded in an HMD as the head-anchored tracking device. Additionally, or alternatively, the head-anchored tracking device may be a camera and/or other suitable positional tracking device that is rigidly mounted or otherwise fixed to the HMD. As shown in FIG. 3, a user wearing the HMD holds a real calibration object having one or more fiducial markers. As further shown in FIG. 3, coordinate systems of the positional tracking device (or camera), the calibration object, and the HMD are respectively represented as {C}, {O}, and {H}. Because the camera is fixed to the HMD, an extrinsic geometric transformation between the camera and the HMD (GHC) is fixed. The point on the calibration object to be aligned with the virtual object is fixed at {right arrow over (q)}_(o) with respect to the coordinate system of {O}. The corresponding point on the virtual object, visualized in the user's view, is at {right arrow over (p)} in the coordinate system associated with the HMD {H}. In some implementations, the positional tracking device may determine a pose of the tracked object (G_(co)), which may eventually yield point sets {q|q_(i)=G_(co,i)·{right arrow over (q)}_(o),i=1, . . . , n} and {p_(i)|i=1, . . . , n} that can be used to compute the transformation function T, as described above. In some implementations, the pose of the tracked object (G_(co)) that eventually yields the point sets may be determined based on a time when the user performs a calibration input to indicate that the points on the calibration object and the virtual object appear to be aligned in the user's view (e.g., within a threshold amount of time before and/or after the user performs the calibration input).

As indicated above, FIG. 3 is provided merely as one or more examples. Other examples may differ from what is described with regard to FIG. 3.

FIG. 4 is a diagram of an example implementation 400 described herein. FIG. 4 shows example views from a perspective of the user when the user is performing the calibration procedure described in further detail above with the head-anchored tracking device configured to perform inside-out positional tracking.

As shown in FIG. 4, and by reference number 410, the virtual object and the real calibration object may be misaligned in the user's view prior to calibration. As shown in FIG. 4, and by reference number 420, the user may be instructed to align one or more features (e.g., corner points) on the calibration object with one or more corresponding features on a virtual target. For example, a first virtual target may be displayed at a first location within the user's field of view. The user may move the calibration object around in space, move a head position and/or a body position, and/or the like until the user is satisfied that the real feature(s) on the calibration object are aligned with the corresponding feature(s) on the first virtual target. In some implementations, the user may perform a calibration input (e.g., pressing a button, clicking a mouse, uttering a voice command, making a hand gesture, and/or the like) to indicate that the real feature(s) on the calibration object appear to be aligned with the corresponding feature(s) on the first virtual target within the user's view. The head-mounted tracking device may provide a measurement indicating a three-dimensional position of the real feature(s) on the calibration object, which may be recorded along with the corresponding feature(s) on the first virtual target.

As further shown in FIG. 4, a second virtual target may then be displayed at a different location in the user's field of view and the user may again be instructed to align the one or more features on the calibration object with the second virtual target. This process may be repeated until a set of measurements having a threshold quantity of points have been collected (e.g., ˜20 repetitions for ˜20 measurements in a single point calibration procedure, ˜4 repetitions for ˜20 measurements in a five-point calibration procedure, and/or the like). In some implementations, the calibration platform may compute the transformation function based on the set of measurements, as described above. As shown in FIG. 4, and by reference number 430, the transformation function can be applied to internal projection operators that the HMD uses to present a two-dimensional image for each eye such that the virtual object is superimposed on the real calibration object.

As indicated above, FIG. 4 is provided merely as one or more examples. Other examples may differ from what is described with regard to FIG. 4.

FIGS. 5A-5B are diagrams of one or more example implementations 500, 510 described herein. FIGS. 5A-5B show a setup for performing the calibration procedure described in further detail above with a world-anchored tracking device configured to perform outside-in positional tracking.

As shown in FIG. 5A, in implementation 500, coordinate systems associated with the world-anchored tracking device, the calibration object, the HMD, and the real-world may be respectively represented as {E}, {O}, {H}, and {W}. A difference between the setup using the head-anchored tracking device (e.g., as shown in FIG. 3) and implementation 500 is that the transformation GHC between the coordinate system of the head-anchored tracking device {C} and the coordinate system of the HMD {H} is fixed, which is not the case for the world-anchored tracking device. Rather, for the world-anchored tracking device, the transformation G_(HE) between the coordinate system of the world-anchored tracking device {E} and the coordinate system of the HMD {H} is expressed as G_(HE)=G_(WH) ⁻¹·G_(WE). Because the world-anchored tracking device is stationary, and therefore does not change a pose within the environment, G_(WE) is fixed. Therefore, the calibration platform may obtain an additional component to maintain and update the transformation G_(WH) between the real-world and the HMD {H} such that the transformation G_(HE) between the positional tracking device and the HMD can be determined.

For example, in some implementations, a SLAM-based spatial mapping capability of the HMD may be used to complete a transformation chain from the tracked calibration object to the user's view. In other words, the transformation from the world-anchored tracking device to the calibration object may be determined because the calibration object is tracked and the external world-anchored tracking device is fixed in the world. The spatial mapping capabilities may provide and update the pose of the HMD with respect to the world, which may close the transformation chain and permit the calibration platform to determine the pose of the calibration object relative to the HMD. In this way, direct line of sight between the camera of the HMD and the calibration object is not needed, as long as the user can see the calibration object to perform the alignment task and the world-anchored tracking device remains in the same fixed position in the world. Accordingly, the HMD spatial mapping may not be reliant on the calibration object, but rather on self-localizing within the environment (e.g., with respect to large features such as walls). Alternatively, if the HMD does not have spatial mapping and/or self-localization capabilities, another method may be used to maintain and update the transformation G_(WH) between the real-world and the HMD {H} (e.g., using the world-anchored tracking device and mounting fiducial markers to also track the HMD). As shown in FIG. 5B, in implementation 510, the setup based on the world-anchored tracking device may use a calibration object attached to a frame composed from passive spherical markers. These spherical markers may be tracked by the world-anchored tracking device and used to determine the three-dimensional position of one or more points on the calibration object that are to be aligned with a virtual object. In some implementations, the three-dimensional position of the one or more points on the calibration object may be determined based on a time when the user performs a calibration input to indicate that the points on the calibration object and the corresponding points on the virtual object appear to be aligned in the user's view.

As indicated above, FIGS. 5A-5B are provided merely as one or more examples. Other examples may differ from what is described with regard to FIGS. 5A-5B.

FIG. 6 is a diagram of an example implementation 600 described herein. FIG. 6 shows example views from a perspective of the user when the user is performing the calibration procedure described in further detail above with the world-anchored tracking device configured to perform outside-in positional tracking.

As shown in FIG. 6, and by reference number 610, the virtual object and the real calibration object may be misaligned in the user's view prior to calibration. As shown in FIG. 6, and by reference number 620, the user may be instructed to align one or more features (e.g., corner points) on the calibration object with one or more corresponding features on a virtual target. For example, a first virtual target may be displayed at a first location within the user's field of view. The user may move the calibration object around in space, move a head position and/or a body position, and/or the like until the user is satisfied that the real feature(s) on the calibration object are aligned with the corresponding feature(s) on the first virtual target. In some implementations, the user may perform a calibration input (e.g., pressing a button, clicking a mouse, uttering a voice command, making a hand gesture, and/or the like) to indicate that the real feature(s) on the calibration object appear to be aligned with the corresponding feature(s) on the first virtual target within the user's view. The head-mounted tracking device may provide a measurement indicating a three-dimensional position of the real feature(s) on the calibration object, which may be recorded along with the corresponding feature(s) on the first virtual target.

As further shown in FIG. 6, a second virtual target may then be displayed at a different location in the user's field of view and the user may again be instructed to align the one or more features on the calibration object with the second virtual target. This process may be repeated until a set of measurements having a threshold quantity of points have been collected (e.g., ˜20 repetitions for ˜20 measurements in a single point calibration procedure, ˜4 repetitions for ˜20 measurements in a five-point calibration procedure, and/or the like). In some implementations, the calibration platform may compute the transformation function based on the set of measurements, as described above. As shown in FIG. 6, and by reference number 630, the transformation function can be applied to internal projection operators that the HMD uses to present a two-dimensional image for each eye such that the virtual object is superimposed on the real calibration object.

As indicated above, FIG. 6 is provided merely as one or more examples. Other examples may differ from what is described with regard to FIG. 6.

FIG. 7 is a diagram of an example implementation 700 described herein. FIG. 7 shows an example calibration setup that may be designed to reduce error that may be caused by poor alignment (e.g., due to hand tremor, user fatigue, and/or the like).

As shown in FIG. 7, and by reference number 710, the real calibration object(s) may be stabilized (e.g., by mounting or otherwise fixing the calibration object(s) to a rigid and/or flexible stand). In this way, the user does not have to hold the calibration object(s), which may reduce or eliminate error due to hand tremor. As further shown in FIG. 7, and by reference number 720, the virtual object may then be displayed relative to one or more of the real calibration objects. Accordingly, because the user is not holding the calibration object(s), the user may move around the real-world environment, shift a head and/or body position, and/or the like, and verify proper alignment from multiple viewpoints. In this way, more accurate and reliable alignment measurements may be obtained because the user is not holding the calibration object and possibly imparting small movements to the calibration object during alignment. Furthermore, in this way, a distance from the calibration object to the HMD is not limited by the user's arm length (e.g., allowing the virtual object to be placed at other three-dimensional locations that are not limited to the space within the user's reach). As shown in FIG. 7, and by reference number 730, the user may align the calibration object with the virtual object and provide an interaction (e.g., a button press, a mouse click, a voice command, a gesture, and/or the like) when the virtual object and the calibration object appear to be aligned in the user's view. In some implementations, based on the user interaction, the calibration platform may record the three-dimensional position of the point(s) on the real calibration object that are to be aligned with the corresponding point(s) on the virtual object.

As indicated above, FIG. 7 is provided merely as one or more examples. Other examples may differ from what is described with regard to FIG. 7.

FIG. 8 is a diagram of an example environment 800 in which systems and/or methods described herein may be implemented. As shown in FIG. 8, environment 800 may include a display device 810, a positional tracking device 820, a calibration platform 830, and a network 840. Devices of environment 800 may interconnect via wired connections, wireless connections, or a combination of wired and wireless connections.

Display device 810 includes any display that is capable of presenting imaging provided by calibration platform 830. Display device 810 may include technologies such as liquid crystal display (LCDs) devices, light-emitting diode (LED) display devices, plasma display devices, wearable display devices (e.g., head-mounted display devices), handheld display devices, and/or the like. For example, in some implementations, display device 810 may include or be part of a wearable display device such as an optical see-through head-mounted display (OST-HMD) device, a video see-through head-mounted display (VST-HMD) device, and/or the like. Additionally, or alternatively, display device 810 may be a non-wearable display device, such as a handheld computer, a tablet computer, and/or the like. In some implementations, display device 810 may be a stereoscopic or three-dimensional display device.

Positional tracking device 820 includes one or more devices capable of receiving, generating, processing, and/or providing information related to a position (e.g., three-dimensional coordinates) of one or more real-world objects. For example, positional tracking device 820 may be a head-anchored tracking device that can perform “inside-out” positional tracking (e.g., a front-facing camera embedded in display device 810, a camera and/or other sensors rigidly mounted on display device 810, and/or the like). Additionally, or alternatively, positional tracking device 820 may be a world-anchored tracking device that can perform “outside-in” positional tracking (e.g., a reflective markers tracking device, an electromagnetic tracking device, a projective light-based tracking device, and/or the like). In some implementations, positional tracking device 820 may be configured to track three-dimensional coordinates of real-world objects (e.g., display device 810, a calibration object, and/or the like) and provide the tracked three-dimensional coordinates to display device 810 and/or calibration platform 830.

Calibration platform 830 includes one or more devices capable of receiving, generating, storing, processing, and/or providing information associated with augmented reality imaging, mixed reality imaging, a position (e.g., a pose) of one or more real-world objects (e.g., a calibration object), and/or the like. For example, calibration platform 830 may include an image processing system of display device 810, an external image processing computing device connected to display device 810 (e.g., via a peripheral cable, via network 840, and/or the like), an image processing platform implemented in a cloud computing environment, and/or the like. In some implementations, calibration platform 830 may provide output to display device 810 for display. In some implementations, calibration platform 830 may compute a 3D-to-3D transformation function that provides a mapping between three-dimensional points in a real-world coordinate system and points used for generating a three-dimensional virtual scene based on measurements gathered using positional tracking device 820. In some implementations, the measurements may be gathered using positional tracking device 820 based on information indicating that a user performed a calibration input.

Network 840 includes one or more wired and/or wireless networks. For example, network 840 may include a cellular network (e.g., a long-term evolution (LTE) network, a code division multiple access (CDMA) network, a 3G network, a 4G network, a 5G network, another type of next generation network, etc.), a public land mobile network (PLMN), a local area network (LAN), a wide area network (WAN), a personal area network (PAN), a body area network (BAN), a metropolitan area network (MAN), a telephone network (e.g., the Public Switched Telephone Network (PSTN)), a private network, an ad hoc network, an intranet, the Internet, a fiber optic-based network, a cloud computing network, and/or the like, and/or a combination of these and/or other types of networks.

The number and arrangement of devices and networks shown in FIG. 8 are provided as one or more examples. In practice, there may be additional devices and/or networks, fewer devices and/or networks, different devices and/or networks, or differently arranged devices and/or networks than those shown in FIG. 8. Furthermore, two or more devices shown in FIG. 8 may be implemented within a single device, or a single device shown in FIG. 8 may be implemented as multiple, distributed devices. Additionally, or alternatively, a set of devices (e.g., one or more devices) of environment 800 may perform one or more functions described as being performed by another set of devices of environment 800.

FIG. 9 is a diagram of example components of a device 900. Device 900 may correspond to display device 810, positional tracking device 820, and/or calibration platform 830. In some implementations, display device 810, positional tracking device 820, and/or calibration platform 830 may include one or more devices 900 and/or one or more components of device 900. As shown in FIG. 9, device 900 may include a bus 910, a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, and a communication interface 970.

Bus 910 includes a component that permits communication among multiple components of device 900. Processor 920 is implemented in hardware, firmware, and/or a combination of hardware and software. Processor 920 is a central processing unit (CPU), a graphics processing unit (GPU), an accelerated processing unit (APU), a microprocessor, a microcontroller, a digital signal processor (DSP), a field-programmable gate array (FPGA), an application-specific integrated circuit (ASIC), or another type of processing component. In some implementations, processor 920 includes one or more processors capable of being programmed to perform a function. Memory 930 includes a random-access memory (RAM), a read only memory (ROM), and/or another type of dynamic or static storage device (e.g., a flash memory, a magnetic memory, and/or an optical memory) that stores information and/or instructions for use by processor 920.

Storage component 940 stores information and/or software related to the operation and use of device 900. For example, storage component 940 may include a hard disk (e.g., a magnetic disk, an optical disk, and/or a magneto-optic disk), a solid-state drive (SSD), a compact disc (CD), a digital versatile disc (DVD), a floppy disk, a cartridge, a magnetic tape, and/or another type of non-transitory computer-readable medium, along with a corresponding drive.

Input component 950 includes a component that permits device 900 to receive information, such as via user input (e.g., a touch screen display, a keyboard, a keypad, a mouse, a button, a switch, and/or a microphone). Additionally, or alternatively, input component 950 may include a component for determining location (e.g., a global positioning system (GPS) component) and/or a sensor (e.g., an accelerometer, a gyroscope, an actuator, another type of positional or environmental sensor, and/or the like). Output component 960 includes a component that provides output information from device 900 (via, e.g., a display, a speaker, a haptic feedback component, an audio or visual indicator, and/or the like).

Communication interface 970 includes a transceiver-like component (e.g., a transceiver, a separate receiver, a separate transmitter, and/or the like) that enables device 900 to communicate with other devices, such as via a wired connection, a wireless connection, or a combination of wired and wireless connections. Communication interface 970 may permit device 900 to receive information from another device and/or provide information to another device. For example, communication interface 970 may include an Ethernet interface, an optical interface, a coaxial interface, an infrared interface, a radio frequency (RF) interface, a universal serial bus (USB) interface, a Wi-Fi interface, a cellular network interface, and/or the like.

Device 900 may perform one or more processes described herein. Device 900 may perform these processes based on processor 920 executing software instructions stored by a non-transitory computer-readable medium, such as memory 930 and/or storage component 940. As used herein, the term “computer-readable medium” refers to a non-transitory memory device. A memory device includes memory space within a single physical storage device or memory space spread across multiple physical storage devices.

Software instructions may be read into memory 930 and/or storage component 940 from another computer-readable medium or from another device via communication interface 970. When executed, software instructions stored in memory 930 and/or storage component 940 may cause processor 920 to perform one or more processes described herein. Additionally, or alternatively, hardware circuitry may be used in place of or in combination with software instructions to perform one or more processes described herein. Thus, implementations described herein are not limited to any specific combination of hardware circuitry and software.

The number and arrangement of components shown in FIG. 9 are provided as an example. In practice, device 900 may include additional components, fewer components, different components, or differently arranged components than those shown in FIG. 9. Additionally, or alternatively, a set of components (e.g., one or more components) of device 900 may perform one or more functions described as being performed by another set of components of device 900.

FIG. 10 is a flow chart of an example process 1000 for aligning a three-dimensional virtual scene and a three-dimensional real world for a stereoscopic head-mounted display device. In some implementations, one or more process blocks of FIG. 10 may be performed by a calibration platform (e.g., calibration platform 830). In some implementations, one or more process blocks of FIG. 10 may be performed by another device or a group of devices separate from or including the calibration platform, such as a display device (e.g., display device 810), a positional tracking device (e.g., positional tracking device 820), and/or the like.

As shown in FIG. 10, process 1000 may include obtaining a set of measurements for aligning a real-world coordinate system associated with a positional tracking device and a display coordinate system corresponding to a three-dimensional display space of an optical see-through head-mounted display device (block 1010). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may obtain a set of measurements for aligning a real-world coordinate system associated with a positional tracking device and a display coordinate system corresponding to a three-dimensional display space of an optical see-through head-mounted display device, as described above.

As further shown in FIG. 10, process 1000 and block 1010 may include causing the optical see-through head-mounted display device to display a three-dimensional virtual object in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device (block 1012). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may cause the optical see-through head-mounted display device to display a three-dimensional virtual object in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device, as described above.

As further shown in FIG. 10, process 1000 and block 1010 may include receiving information from the positional tracking device that relates to a current pose of a three-dimensional real-world object to be aligned with the three-dimensional virtual object (block 1014). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may receive information from the positional tracking device that relates to a current pose of a three-dimensional real-world object to be aligned with the three-dimensional virtual object, as described above.

As further shown in FIG. 10, process 1000 and block 1010 may include recording a three-dimensional position of a plurality of points on the three-dimensional real-world object in the real-world coordinate system based on the current pose of the three-dimensional real-world object based on an indication that the plurality of points on the three-dimensional real-world object respectively correspond with a plurality of points on the three-dimensional virtual object (block 1016). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may record a three-dimensional position of a plurality of points on the three-dimensional real-world object in the real-world coordinate system based on the current pose of the three-dimensional real-world object based on an indication that the plurality of points on the three-dimensional real-world object respectively correspond with a plurality of points on the three-dimensional virtual object, as described above.

As further shown in FIG. 10, process 1000 and block 1010 may include generating the set of measurements based on the three-dimensional position of the plurality of points on the three-dimensional real-world object in the real-world coordinate system (block 1018). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may generate the set of measurements based on the three-dimensional position of the plurality of points on the three-dimensional real-world object in the real-world coordinate system, as described above.

As further shown in FIG. 10, process 1000 may include generating a transformation function that permits the calibration platform to provide a mapping between three-dimensional points in the real-world coordinate system and three-dimensional points in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device based on the set of measurements (block 1020). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may generate a transformation function that permits the calibration platform to provide a mapping between three-dimensional points in the real-world coordinate system and three-dimensional points in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device based on the set of measurements, as described above.

Process 1000 may include additional implementations, such as any single implementation or any combination of implementations described below and/or in connection with one or more other processes described elsewhere herein.

In some implementations, the transformation function may be a linear transformation represented using a four by four (4×4) matrix applied to left eye and right eye internal projection matrices associated with the optical see-through head-mounted display device. In some implementations, the transformation function may include one or more of an affine transformation, a perspective transformation, or an isometric transformation. In some implementations, the transformation function may be generated based on one or more of a Random Sample Consensus (RANSAC) algorithm or a Direct Linear Transformation (DLT) algorithm with an objective of minimizing a reprojection error of the set of measurements. In some implementations, generating the set of measurements may comprise discarding, from the set of measurements, one or more outliers based on a reprojection error of the set of measurements.

In some implementations, the positional tracking device may comprise a camera that is coupled to the optical see-through head-mounted display device and/or a camera positioned at a particular location external to the optical see-through head-mounted display device. In some implementations, the plurality of points on the three-dimensional real-world object may comprise at least three non-collinear or non-coplanar points corresponding to at least three points on the three-dimensional virtual object.

Although FIG. 10 shows example blocks of process 1000, in some implementations, process 1000 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in FIG. 10. Additionally, or alternatively, two or more of the blocks of process 1000 may be performed in parallel.

FIG. 11 is a flow chart of an example process 1100 for aligning a three-dimensional virtual scene and a three-dimensional real world for a stereoscopic head-mounted display device. In some implementations, one or more process blocks of FIG. 11 may be performed by a calibration platform (e.g., calibration platform 830). In some implementations, one or more process blocks of FIG. 11 may be performed by another device or a group of devices separate from or including the calibration platform, such as a display device (e.g., display device 810), a positional tracking device (e.g., positional tracking device 820), and/or the like.

As shown in FIG. 11, process 1100 may include receiving, from a positional tracking device, information that relates to a pose of a three-dimensional real-world object to be aligned with a three-dimensional virtual object (block 1110). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may receive, from a positional tracking device, information that relates to a pose of a three-dimensional real-world object to be aligned with a three-dimensional virtual object, as described above.

As shown in FIG. 11, process 1100 may include performing a first operation to display, via an optical see-through head-mounted display device, the three-dimensional virtual object in a display coordinate system corresponding to a three-dimensional display space of the optical see-through head-mounted display device (block 1120). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may perform a first operation to display, via an optical see-through head-mounted display device, the three-dimensional virtual object in a display coordinate system corresponding to a three-dimensional display space of the optical see-through head-mounted display device, as described above.

As shown in FIG. 11, process 1100 may include performing a second operation to record three-dimensional positions of multiple points on the three-dimensional real-world object in a real-world coordinate system associated with the positional tracking device based on the pose of the three-dimensional real-world object at a time when a calibration input is received (block 1130). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may perform a second operation to record three-dimensional positions of multiple points on the three-dimensional real-world object in a real-world coordinate system associated with the positional tracking device based on the pose of the three-dimensional real-world object at a time when a calibration input is received, as described above.

As shown in FIG. 11, process 1100 may include repeating the first operation and the second operation until a recorded quantity of the three-dimensional positions satisfies a threshold value (block 1140). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may repeat the first operation and the second operation until a recorded quantity of the three-dimensional positions satisfies a threshold value, as described above.

As shown in FIG. 11, process 1100 may include generating a transformation function to provide a mapping between three-dimensional points in the real-world coordinate system and three-dimensional points in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device based on the recorded quantity of the three-dimensional positions (block 1150). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may generate a transformation function to provide a mapping between three-dimensional points in the real-world coordinate system and three-dimensional points in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device based on the recorded quantity of the three-dimensional positions, as described above.

Process 1100 may include additional implementations, such as any single implementation or any combination of implementations described below and/or in connection with one or more other processes described elsewhere herein.

In some implementations, the multiple points on the three-dimensional real-world object may correspond to corners of a real cube and the multiple corresponding points on the three-dimensional virtual object may correspond to corners of a virtual cube. In some implementations, the three-dimensional real-world object may have multiple colored faces with fiducial markers that are tracked by the positional tracking device, and the three-dimensional virtual object may have multiple colored faces that correspond to the multiple colored faces of the three-dimensional real-world object.

In some implementations, the transformation function includes one or more of an affine transformation, a perspective transformation, or an isometric transformation.

In some implementations, the positional tracking device may be a camera coupled to the optical see-through head-mounted display device. In some implementations, the positional tracking device may be positioned at a particular location external to the optical see-through head-mounted display device.

In some implementations, the multiple points on the three-dimensional real-world object may comprise at least three non-collinear points or non-coplanar points corresponding to at least three points on the three-dimensional virtual object.

Although FIG. 11 shows example blocks of process 1100, in some implementations, process 1100 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in FIG. 11. Additionally, or alternatively, two or more of the blocks of process 1100 may be performed in parallel.

FIG. 12 is a flow chart of an example process 1200 for aligning a three-dimensional virtual scene and a three-dimensional real world for a stereoscopic head-mounted display device. In some implementations, one or more process blocks of FIG. 12 may be performed by a calibration platform (e.g., calibration platform 830). In some implementations, one or more process blocks of FIG. 12 may be performed by another device or a group of devices separate from or including the calibration platform, such as a display device (e.g., display device 810), a positional tracking device (e.g., positional tracking device 820), and/or the like.

As shown in FIG. 12, process 1200 may include generating a transformation function to provide a mapping between three-dimensional points in a real-world coordinate system and three-dimensional points in a display coordinate system corresponding to a three-dimensional display space of an optical see-through head-mounted display device based on a set of measurements gathered using a positional tracking device (block 1210). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may generate a transformation function to provide a mapping between three-dimensional points in a real-world coordinate system and three-dimensional points in a display coordinate system corresponding to a three-dimensional display space of an optical see-through head-mounted display device based on a set of measurements gathered using a positional tracking device, as described above.

As shown in FIG. 12, process 1200 may include applying the transformation function to a first internal projection operator to produce a first corrected projection operator that the optical see-through head-mounted display device uses to display a first two-dimensional perspective image for a left eye (block 1220). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may apply the transformation function to a first internal projection operator to produce a first corrected projection operator that the optical see-through head-mounted display device uses to display a first two-dimensional perspective image for a left eye, as described above.

As shown in FIG. 12, process 1200 may include applying the transformation function to a second internal projection operator to produce a second corrected projection operator that the optical see-through head-mounted display device uses to display a second two-dimensional perspective image for a right eye (block 1230). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may apply the transformation function to a second internal projection operator to produce a second corrected projection operator that the optical see-through head-mounted display device uses to display a second two-dimensional perspective image for a right eye, as described above.

As shown in FIG. 12, process 1200 may include displaying, via the optical see-through head-mounted display device, a three-dimensional image in the display coordinate system by presenting the first two-dimensional perspective image based on the first corrected projection operator and presenting the second two-dimensional perspective image based on the second corrected projection operator, wherein the three-dimensional image in the display coordinate system may be superimposed on an object in the real-world coordinate system (block 1240). For example, the calibration platform (e.g., using a processor 920, a memory 930, a storage component 940, an input component 950, an output component 960, a communication interface 970, and/or the like) may display, via the optical see-through head-mounted display device, a three-dimensional image in the display coordinate system by presenting the first two-dimensional perspective image based on the first corrected projection operator and presenting the second two-dimensional perspective image based on the second corrected projection operator. In some implementations, the three-dimensional image in the display coordinate system may be superimposed on an object in the real-world coordinate system.

Process 1200 may include additional implementations, such as any single implementation or any combination of implementations described below and/or in connection with one or more other processes described elsewhere herein.

In some implementations, the transformation function may include an affine transformation matrix, a perspective transformation matrix, and/or an isometric transformation matrix to minimize a reprojection error associated with the set of measurements.

In some implementations, the positional tracking device may be a camera coupled to the optical see-through head-mounted display device. In some implementations, the positional tracking device may be positioned at a particular location external to the optical see-through head-mounted display device.

Although FIG. 12 shows example blocks of process 1200, in some implementations, process 1200 may include additional blocks, fewer blocks, different blocks, or differently arranged blocks than those depicted in FIG. 12. Additionally, or alternatively, two or more of the blocks of process 1200 may be performed in parallel.

The foregoing disclosure provides illustration and description but is not intended to be exhaustive or to limit the implementations to the precise forms disclosed. Modifications and variations may be made in light of the above disclosure or may be acquired from practice of the implementations.

As used herein, the term “component” is intended to be broadly construed as hardware, firmware, and/or a combination of hardware and software.

Some implementations are described herein in connection with thresholds. As used herein, satisfying a threshold may, depending on the context, refer to a value being greater than the threshold, more than the threshold, higher than the threshold, greater than or equal to the threshold, less than the threshold, fewer than the threshold, lower than the threshold, less than or equal to the threshold, equal to the threshold, or the like.

Certain user interfaces have been described herein and/or shown in the figures. A user interface may include a graphical user interface, a non-graphical user interface, a text-based user interface, and/or the like. A user interface may provide information for display. In some implementations, a user may interact with the information, such as by providing input via an input component of a device that provides the user interface for display. In some implementations, a user interface may be configurable by a device and/or a user (e.g., a user may change the size of the user interface, information provided via the user interface, a position of information provided via the user interface, etc.). Additionally, or alternatively, a user interface may be pre-configured to a standard configuration, a specific configuration based on a type of device on which the user interface is displayed, and/or a set of configurations based on capabilities and/or specifications associated with a device on which the user interface is displayed.

It will be apparent that systems and/or methods described herein may be implemented in different forms of hardware, firmware, or a combination of hardware and software. The actual specialized control hardware or software code used to implement these systems and/or methods is not limiting of the implementations. Thus, the operation and behavior of the systems and/or methods are described herein without reference to specific software code—it being understood that software and hardware can be designed to implement the systems and/or methods based on the description herein.

Even though particular combinations of features are recited in the claims and/or disclosed in the specification, these combinations are not intended to limit the disclosure of various implementations. In fact, many of these features may be combined in ways not specifically recited in the claims and/or disclosed in the specification. Although each dependent claim listed below may directly depend on only one claim, the disclosure of various implementations includes each dependent claim in combination with every other claim in the claim set.

No element, act, or instruction used herein should be construed as critical or essential unless explicitly described as such. Also, as used herein, the articles “a” and “an” are intended to include one or more items, and may be used interchangeably with “one or more.” Furthermore, as used herein, the term “set” is intended to include one or more items (e.g., related items, unrelated items, a combination of related and unrelated items, etc.), and may be used interchangeably with “one or more.” Where only one item is intended, the phrase “only one” or similar language is used. Also, as used herein, the terms “has,” “have,” “having,” or the like are intended to be open-ended terms. Further, the phrase “based on” is intended to mean “based, at least in part, on” unless explicitly stated otherwise. 

What is claimed is:
 1. A method, comprising: obtaining, by a calibration platform, a set of measurements for aligning a real-world coordinate system associated with a positional tracking device and a display coordinate system corresponding to a three-dimensional display space of an optical see-through head-mounted display device, wherein obtaining the set of measurements comprises: causing, by the calibration platform, the optical see-through head-mounted display device to display a three-dimensional virtual object in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device; receiving, at the calibration platform, information from the positional tracking device that relates to a current pose of a three-dimensional real-world object to be aligned with the three-dimensional virtual object; recording, by the calibration platform, a three-dimensional position of a plurality of points on the three-dimensional real-world object in the real-world coordinate system based on the current pose of the three-dimensional real-world object based on an indication that the plurality of points on the three-dimensional real-world object respectively corresponds with a plurality of points on the three-dimensional virtual object; and generating the set of measurements based on the three-dimensional position of the plurality of points on the three-dimensional real-world object in the real-world coordinate system; and generating, by the calibration platform, a transformation function that permits the calibration platform to provide a mapping between three-dimensional points in the real-world coordinate system and three-dimensional points in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device based on the set of measurements.
 2. The method of claim 1, wherein the transformation function is a linear transformation represented using a four by four matrix applied to left eye and right eye internal projection matrices associated with the optical see-through head-mounted display device.
 3. The method of claim 1, wherein the transformation function includes one or more of an affine transformation, a perspective transformation, or an isometric transformation.
 4. The method of claim 1, wherein the transformation function is generated based on one or more of a Random Sample Consensus (RANSAC) algorithm or a Direct Linear Transformation (DLT) algorithm with an objective of minimizing a reprojection error of the set of measurements.
 5. The method of claim 1, wherein generating the set of measurements comprises: discarding, from the set of measurements, one or more outliers based on a reprojection error of the set of measurements.
 6. The method of claim 1, wherein the positional tracking device comprises a camera that is coupled to the optical see-through head-mounted display device or positioned at a particular location external to the optical see-through head-mounted display device.
 7. The method of claim 1, wherein the plurality of points on the three-dimensional real-world object comprise at least three non-collinear or non-coplanar points corresponding to at least three points on the three-dimensional virtual object.
 8. A calibration device, comprising: a memory; and one or more processors, communicatively coupled to the memory, to: receive, from a positional tracking device, information that relates to a pose of a three-dimensional real-world object to be aligned with a three-dimensional virtual object; perform a first operation to display, via an optical see-through head-mounted display device, the three-dimensional virtual object in a display coordinate system corresponding to a three-dimensional display space of the optical see-through head-mounted display device; perform a second operation to record three-dimensional positions of multiple points on the three-dimensional real-world object in a real-world coordinate system associated with the positional tracking device based on the pose of the three-dimensional real-world object at a time when a calibration input is received; repeat the first operation and the second operation until a recorded quantity of the three-dimensional positions satisfies a threshold value; and generate a transformation function to provide a mapping between three-dimensional points in the real-world coordinate system and three-dimensional points in the display coordinate system corresponding to the three-dimensional display space of the optical see-through head-mounted display device based on the recorded quantity of the three-dimensional positions.
 9. The calibration device of claim 8, wherein the multiple points on the three-dimensional real-world object correspond to corners of a real cube and the multiple corresponding points on the three-dimensional virtual object correspond to corners of a virtual cube.
 10. The calibration device of claim 8, wherein the three-dimensional real-world object has multiple colored faces with fiducial markers that are tracked by the positional tracking device, and wherein the three-dimensional virtual object has multiple colored faces that correspond to the multiple colored faces of the three-dimensional real-world object.
 11. The calibration device of claim 8, wherein the transformation function includes one or more of an affine transformation, a perspective transformation, or an isometric transformation.
 12. The calibration device of claim 8, wherein the positional tracking device is a camera coupled to the optical see-through head-mounted display device.
 13. The calibration device of claim 8, wherein the positional tracking device is positioned at a particular location external to the optical see-through head-mounted display device.
 14. The calibration device of claim 8, wherein the multiple points on the three-dimensional real-world object comprise at least three non-collinear points or non-coplanar corresponding to at least three points on the three-dimensional virtual object.
 15. A non-transitory computer-readable medium storing instructions comprising: one or more instructions that, when executed by one or more processors, cause the one or more processors to: generate a transformation function to provide a mapping between three-dimensional points in a real-world coordinate system to three-dimensional points in a display coordinate system corresponding to a three-dimensional display space of an optical see-through head-mounted display device based on a set of measurements gathered using a positional tracking device; apply the transformation function to a first internal projection operator to produce a first corrected projection operator that the optical see-through head-mounted display device uses to display a first two-dimensional perspective image for a left eye; apply the transformation function to a second internal projection operator to produce a second corrected projection operator that the optical see-through head-mounted display device uses to display a second two-dimensional perspective image for a right eye; and display, via the optical see-through head-mounted display device, a three-dimensional image in the display coordinate system by presenting the first two-dimensional perspective image based on the first corrected projection operator and presenting the second two-dimensional perspective image based on the second corrected projection operator, wherein the three-dimensional image in the display coordinate system is superimposed on an object in the real-world coordinate system.
 16. The non-transitory computer-readable medium of claim 15, wherein the transformation function includes an affine transformation matrix to minimize a reprojection error associated with the set of measurements.
 17. The non-transitory computer-readable medium of claim 15, wherein the transformation function includes a perspective transformation matrix to minimize a reprojection error associated with the set of measurements.
 18. The non-transitory computer-readable medium of claim 15, wherein the transformation function includes an isometric transformation matrix to minimize a reprojection error associated with the set of measurements.
 19. The non-transitory computer-readable medium of claim 15, wherein the positional tracking device is a camera coupled to the optical see-through head-mounted display device.
 20. The non-transitory computer-readable medium of claim 15, wherein the positional tracking device is positioned at a particular location external to the optical see-through head-mounted display device. 